You are engaging in a logical fallacy, that of a false either/or dilemma, as if salvation by faith means that one considers obedience superfluous, as if faith and obedience to the object of faith can be separated in effect, and ignoring that the issue is which is the cause of justification, which is faith in the Lord Jesus is imputed for righteousness, and effects obedience by the Spirit, and in this sense they both go together, as both Jesus, Paul and James teach.
Rather than sola fide meaning salvation by a mere inert, ineffectual faith, as if one can actually believe on the Lord Jesus Christ for salvation and not have it also effect his life, or that one is justified by actually becoming good in heart (as per Rome), it is penitent, heart-purifying, regenerating effectual faith, (Acts 10:43-47; 15:7-9) which is imputed for righteousness, (Romans 4:5) and is shown in baptism and following the Lord, (Acts 2:38-47; Jn. 10:27,28) who was sent by the Father to be the savior of the world. (1 John 4:14)
And by which faith the redeemed soul is "accepted in the Beloved" and positionally seated with Him in Heaven, on His account, glory to God. (Ephesians 1:6; 2:6; cf. Phil. 3:21) And those who die in that obedient faith will go to be forever with Him at death or His return (Phil 1:23; 2Cor. 5:8 [“we”]; Heb, 12:22,23; 1Cor. 15:51ff'; 1Thess. 4:17) In contrast to those who were never born of the Spirit or who terminally fall away. (Gal. 5:1-4; Heb. 3:12; 10:25-39; 2 Corinthians 6:1; 1 Thessalonians 3:5) Thus a very good man needed salvation, and was told by Peter, "To him give all the prophets witness, that through his name whosoever believeth in him shall receive remission of sins." (Acts 10:43)
And which he manifestly did, magnifying God, (Acts 10:46) attesting to salvation, "For with the heart man believeth unto righteousness; and with the mouth confession is made unto ["indicating the point reached or entered" - Strong's], salvation." (Romans 10:10) "And God, which knoweth the hearts, bare them witness, giving them the Holy Ghost, even as he did unto us; And put no difference between us and them, purifying their hearts by faith. (Acts 15:8-9)
And these faith-washed, Spirit sanctified and imputation-justified souls (cf. Rm. 4:5; 1 Corinthians 6:11) were baptized, which is a confession of faith in the Lord Jesus by "body language,' confirmatory of saving faith, (cf. Mk. 16:16) as was that of previously justified Abraham (Gn. 15:6) in later offering up his beloved son, (Genesis 22) which confirmed/vindicated/justified him as being a true believer.
For faith and obedience by the Spirit (Rm. 8:14) go together as cause and effect as does forgiveness and healing in Mark 2 (thus used interchangeably as "Whether is it easier to say to the sick of the palsy, Thy sins be forgiven thee; or to say, Arise, and take up thy bed, and walk?" Mark 2:9). However, the effect is not be to confused as the cause.
Penitent, heart-purifying, regenerating effectual faith, (Acts 10:43-47; 15:7-9) is what is imputed for righteousness, (Romans 4:5) and which is shown in baptism and following the Divine Lord Jesus, (Acts 2:38-47; Jn. 10:27,28) who was sent by the Father to be the savior of the world. (1 John 4:14) And by which faith the redeemed soul is "accepted in the Beloved" and positionally seated with Him in Heaven, on His account, glory to God. (Ephesians 1:6; 2:6; cf. Phil. 3:21) To whom the true believer will directly go to be forever with, at death or at His return, whatever comes first (1 Thessalonians 4:17 cf. Phil 1:23; 2Cor. 5:8) - if the convert dies in that obedient faith, in contrast to eternal punishment for those who were never converted/regenerated, or who terminally fell away after having received so great salvation by obedient faith. (Gal. 5:1-5; Heb. 3:12; 10:25-31, 38-39; 1 Thessalonians 3:5)
This union of faith and works as cause and effect, but not confusing effect with cause, is not some new teaching of sola fide. See Reformation on faith and works , by the grace of God.
Which is in contrast to the RC process of salvation which begins at baptism, which act itself (ex opere operato) is imagined as actually making one righteous enough so that the baptized could go to Heaven if he died right then, before the sin nature that remains makes it manifest that he is not fit to enter Heaven, and which thus (usually) necessitates Purgatory, so that he may once again become good enough to be with God. To wit (emphasis throughout is mine): Baptism is a bath that purifies, justifies, and sanctifies. (CCC 1227) The Most Holy Trinity gives the baptized sanctifying grace, the grace of justification... (CCC 1266) Justification is conferred in Baptism, the sacrament of faith. It conforms us to the righteousness of God, who makes us inwardly just by the power of his mercy. (CCC 1992) The grace of Christ is the gratuitous gift...infused by the Holy Spirit into our soul to heal it of sin and to sanctify it. It is the sanctifying or deifying grace received in Baptism. (CCC 1999)
Although the sinner is justified by the justice of Christ, inasmuch as the Redeemer has merited for him the grace of justification (causa meritoria), nevertheless he is formally justified and made holy by his own personal justice and holiness (causa formalis).” (Catholic Encyclopedia>Sanctifying Grace)
Thus it is believed that the newly baptized, who are thus inwardly just, formally justified and made holy by their own personal justice and holiness, would go to Heaven if they died before they sin:
By virtue of our apostolic authority, we define the following: According to the general disposition of God, the souls of all the saints . . . and other faithful who died after receiving Christ's holy Baptism (provided they were not in need of purification when they died, . . .) have been, are and will be in heaven, in the heavenly Kingdom and celestial paradise with Christ, joined to the company of the holy angels. (CCC 1023)
However, since the unholy sinful Adamic nature is all too alive and manifests itself in these "inwardly just" (righteous souls), meaning that unless they died having attained to the level of practical perfection needed, then they are in in need of purification when they die:
Yet certain temporal consequences of sin remain in the baptized , such as suffering, illness, death, and such frailties inherent in life as weaknesses of character, and so on, as well as an inclination to sin that Tradition calls concupiscence. .. (CCC 1264)
And thus, what flows from the original error of believing man must actually become good enough to be with God (rather than faith being counted/imputed for righteous, - Rm. 4:5 - and with obedience and holiness being evidential fruit of regenerating faith) is that of the doctrine of RC Purgatory, by which, besides atoning for sins not sufficiently expiated on earth, serves to make the baptized good enough to be with God.
The Catholic Encyclopedia also states that St. Augustine "describes two conditions of men; "some there are who have departed this life, not so bad as to be deemed unworthy of mercy, nor so good as to be entitled to immediate happiness " etc. (City of God XXI.24.)
And thus by the close of the fourth century was taught "a place of purgation..from which when purified they "were admitted unto the Holy Mount of the Lord". For " they were "not so good as to be entitled to eternal happiness ".
One "cannot approach God till the purging fire shall have cleansed the stains with which his soul was infested." (Catholic Encyclopedia>Purgatory)
All who die in God's grace and friendship, but still imperfectly purified, are indeed assured of their eternal salvation; but after death they undergo purification, so as to achieve the holiness necessary to enter the joy of heaven. (CCC 1030)
"The purpose of purgatory is to bring you up the level of spiritual excellence needed to experience the full-force presence of God." (Jimmy Akin, How to Explain Purgatory to Protestants).
"Every trace of attachment to evil must be eliminated, every imperfection of the soul corrected." Purification must be complete..." "This is exactly what takes place in Purgatory." — John Paul II, Audiences, 1999; http://w2.vatican.va/content/john-paul-ii/en/audiences/1999/documents/hf_jp-ii_aud_04081999.html
Catholic professor Peter Kreeft states,
"...we will go to Purgatory first, and then to Heaven after we are purged of all selfishness and bad habits and character faults." Peter Kreeft, Because God Is Real: Sixteen Questions, One Answer, p. 224
However, this premise of perfection of character for final salvation eliminates the newly baptized from entering Heaven (if they died before they sinned), since while innocent (not that the act of baptism actually regenerates, as Catholicism teaches), yet they have not yet attained to "spiritual excellence," to elmination of "every trace of attachment to evil," to "perfection of the soul," to the level of practical holiness necessary to enter the joy of heaven.
And this premise would also exclude the contrite criminal of Luke 23:43 from being with Christ at death, yet who was told by the Lord that he would be with Christ in Paradise that day. And likewise imperfect Paul, (Philippians 3:13) who attested that to be absent from the body was to be present with the Lord. (2 Corinthians 5:7; cf. Philippians 1:23) And indeed it would exclude all believers who were told that they would be forever with the Lord if He returned in their lifetime (1 This. 4:17) though they were still undergoing growth in grace, as was Paul.
In contrast, wherever Scripture clearly speak of the next conscious reality for believers then it is with the Lord, (Lk. 23:43 [cf. 2Cor. 12:4; Rv. 2:7]; Phil 1:23; 2Cor. 5:8 [“we”]; 1Cor. 15:51ff'; 1Thess. 4:17)
And rather than Purgatory conforming souls to Christ to inherit the kingdom of God, the next transformative experience that is manifestly taught is that of being made like Christ in the resurrection. (1Jn. 3:2; Rm. 8:23; 1Co 15:53,54; 2Co. 2-4) At which time is the judgment seat of Christ And which is the only suffering after this life, which does not begin at death, but awaits the Lord's return, (1 Corinthians 4:5; 2 Timothy. 4:1,8; Revelation 11:18; Matthew 25:31-46; 1 Peter 1:7; 5:4) and is the suffering of the loss of rewards (and the Lord's displeasure!) due to the manner of material one built the church with. But which one is saved despite the loss of such, not because of. (1 Corinthians 3:8ff)
Note also that the tradition-based Eastern Orthodox reject RC Purgatory, among some other substantial RC distinctives
In addition, the whole premise that suffering itself perfects a person is specious, since testing of character requires being able to choose btwn alternatives, and which this world provides. Thus it is only this world that Scripture peaks of here development of character, such as "Wherein ye greatly rejoice, though now for a season, if need be, ye are in heaviness through manifold temptations." (1 Peter 1:6) The Lord Jesus, in being "made perfect" (Hebrews 2:10) as regards experientially "in all points tempted like as we are, yet without sin" (Hebrews 4:15) was subjected to this in the life.